Thought Bubble Dot Art

Copy & Paste Thought Bubble Dot Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠳⠴⠛⠛⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠉⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠛⢶⡄⠀⠀⠀⠀ ⠀⠀⢀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠀⠀ ⢠⡾⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃ ⠈⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⠀ ⢰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀ ⠀⠙⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠙⠓⠒⠛⠳⠦⠤⠤⠖⠉⠳⢤⣄⣀⣤⡴⠟⠁⡔⠂⠒⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⢱⠁⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠦⣀⠀ ⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞ ⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠋⠀ ⠀⠈⠓⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠚⠉⢪⠓⠦⢄⣀⠤⠴⠒⠦⣄⣀⠀⢀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⣜⢦⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⢲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠈⠙⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠶⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀ ⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿ ⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀ ⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠤⠶⠶⠛⠉⠀⠀⠀ ⠀⠀⠈⠛⠶⠶⠤⠴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⠶⠶⣾⡻⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠈⣷⠀⠉⠙⠛⠒⠒⠒⠛⠋⠁⠀⠈⠛⠳⠦⣤⣤⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣄⢻⣦⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣏⠀⢹⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣟⣿⠙⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⣿⣦⡀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠙⣿⠿⠛⠉⠀⠀⠈⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠉⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠈⠉⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣶⣶⠶⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣶⣤⡀⠀⠀⠀ ⢀⣴⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀ ⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀ ⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀ ⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠁⠀⠀⠀⠀ ⠀⢀⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀ ⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠃⠀⠀⠀ ⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠻⠿⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠒⠺⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⣀⠀⠀⢀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⠻⣿⣷⣶⣤⣀⣀⣠⣤⣶⡾⠟⠀⠹⣿⣦⣄⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⠋⠀⠀⣰⡟⠋⠉⠉⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠹⣆⠁⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠛⠁⢰⠟⠋⠟⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣱⣾⠇

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣳⣛⡉⢉⠉⢉⠉⠉⡙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⣿⠿⠛⠛⡉⠄⠌⠠⠁⠌⢂⠐⠄⢂⠀⡉⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⡱⢂⠁⡐⠠⢁⡐⠈⠄⠡⠈⢌⣤⡈⠌⠄⡂⠄⠡⠈⠳⡄⠀⠀⠀ ⠀⠀⣰⠋⡄⠂⡄⢂⣤⣥⣆⠠⠉⠄⠡⠁⠌⠻⣿⣦⣐⡈⠌⡐⢁⠂⡙⣆⠀⠀ ⠀⢰⠇⠢⢀⠃⠄⢿⣿⣿⣿⠇⡈⠄⠡⣾⣿⣿⣯⣙⠛⢁⠂⠌⣀⠒⠠⠘⡆⠀ ⠀⡾⢀⠃⡄⠡⠌⡈⠙⢋⠡⠐⠠⠈⠄⠻⣿⣿⠿⠁⡐⠠⢈⠐⠠⢈⠔⡁⢸⣀ ⢸⣧⠀⠆⡄⢁⠂⠄⡁⠂⠄⠡⢈⠁⠊⢄⠠⠀⡄⢂⠁⠆⠡⢈⠁⠢⠐⡀⢂⢱ ⠘⡇⠂⠆⡐⣦⠾⢦⡡⠿⠿⠿⢿⣷⣮⣄⢂⠡⠐⡠⠉⠤⢁⠂⠡⡁⠜⡀⠂⢸ ⠀⢿⠀⡃⠄⣷⠀⠀⢹⡔⡐⠢⡀⠄⡉⠿⣿⢆⡁⠆⡡⠒⠠⠈⡅⠰⠐⠠⠐⠑ ⠄⠸⣇⡒⠄⡽⠀⠌⠸⣇⠰⣡⣰⠼⠖⠛⠉⡈⢳⡆⠡⠌⡁⠂⠤⢁⡘⢠⠇⠀ ⠀⠘⣿⣆⡸⠁⠄⠂⠄⠉⢋⠉⡀⠄⠂⠌⢐⣠⠾⢁⠢⠁⠔⡉⠐⣠⢠⠏⠀⠀ ⠀⠸⣿⡙⡇⠐⡈⠐⡈⠐⡀⢂⠐⡈⠄⠘⢻⡁⠂⠆⠡⢉⠐⢠⢁⡴⠋⠀⠀⠀ ⠀⠀⣿⣇⡇⠐⡀⠁⠄⠡⠐⡀⠂⠄⡈⠐⢸⠠⠉⡄⠃⢄⣚⡵⠋⠀⠀⠀⠀⠀ ⠀⠀⢻⡿⣽⡀⠠⠁⠌⠠⠁⠄⡁⠂⠤⠁⢠⡁⠢⢴⡾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣟⣿⣦⣌⡠⠁⠌⠐⢠⣁⣤⠴⢋⣀⣤⢞⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⠀⠙⣆⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢷⡀⠈⠧⡀ ⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠁⠀⠀⢳ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠛⣷⣤⣸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸ ⡇⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⢸ ⡇⠀⠀⠀⠈⢧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠙⢦⡘⠉⠀⢠⠖⡿⢸ ⡇⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢳⡀⣠⠋⣼⠀⡘ ⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠿⠁⠀⠉⠛⡇ ⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣽ ⠘⣦⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡏ ⠀⠈⠓⠦⣤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠀⠀⡤⠏⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠶⠤⣤⣀⣀⣀⣀⡀⣀⣀⣤⣴⠋⠁⠀⠉⠑⠛⠉⠁⠀⠀

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⠀⠀⠀⠀⢀⢤⣔⠕⢂⣀⠴⠂⠀⠈⠉⠙⠒⠚⠯⠽⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡨⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢵⣦⠀⠀⠀⠀⠀ ⠀⠀⠺⠒⡔⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣵⡄⠀⠀⠀ ⠀⣀⣤⡌⠀⠀⡀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⣷⡄⠀⠀ ⢀⣾⡟⠀⠀⠰⠀⡨⠎⡅⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠀⠀⠀⣆⠀⢸⣷⠀⠀ ⣿⡿⠃⠀⠀⣗⣈⣀⠀⢧⠀⠀⠀⠀⡰⠁⠀⢇⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠇⠀ ⡿⣀⠀⠀⢸⠋⣿⣿⣿⡿⢦⡀⠶⢴⣥⣠⣄⡈⢆⠀⠀⠀⠀⠀⠀⠣⡀⢇⠇⠀ ⠉⠺⣽⣦⣀⡆⣆⠛⣱⠃⠀⠈⠁⢠⢟⣿⠿⡟⠿⢲⠀⠀⠀⠀⢀⣠⠔⢋⠀⠀ ⠀⢸⢻⠁⡇⠀⠈⠉⠁⠀⠀⠀⠀⠘⢆⣉⡴⠁⢀⠃⠀⣀⠄⣰⡟⠀⠀⠀⠑⡅ ⠀⣾⡏⠀⠍⢢⡄⠐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠐⢳⠶⠧⠤⡴⠛⣀⣉⠙⢿⢿⠚ ⠀⣿⡇⠀⠄⣸⡀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢀⣠⡼⠁⠀⠀⢰⡀⠈⠻⡿⣴⠊⠀ ⠀⠸⣿⡀⠀⡏⠉⠒⢒⣿⠏⢿⣉⡮⠝⠛⠷⡤⠃⠀⡐⠀⢸⣿⣦⢤⣬⣺⣷⠀ ⠀⠀⠙⣷⡾⠁⠀⠀⢸⣤⠷⠫⢥⣖⠂⠉⠉⢳⡶⠊⠀⢀⣿⠇⠀⠉⠁⠉⠉⠀ ⠀⠀⠀⢹⣧⡀⠀⢂⡏⠀⠂⠀⠀⠈⠳⡄⣠⠮⠤⠄⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢭⡟⣉⣦⣼⣶⡦⠤⢤⣧⣀⣁⣶⠄⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠉⠉⠉⠛⠛⠳⠶⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣺⣕⢦⠀⠀⠂⢀⡴⣶⣯⣟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣇⠀⠀⣼⢹⣿⣿⣿⣿⡌⢳⡄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⣦⢻⣿⣿⡯⠀⠀⠹⣾⣿⣿⣿⣿⡟⢀⡿⠂⢄⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⢸⡌⠙⠒⠋⠀⠀⠀⠀⠀⠙⠛⠿⠷⠚⠋⡠⡀⠀⠱⠀⠀⣼⠃ ⠀⠀⡞⢻⣾⣦⣀⠻⣤⣤⣀⠤⠤⠤⢤⣤⠀⠡⡀⠀⠀⠱⡑⠑⠀⢘⣠⠾⠁⠀ ⡔⢹⡷⣾⣄⠀⠈⠲⣏⠀⡿⠛⢳⣄⠀⠀⠀⠀⠈⢂⣀⣠⣤⠶⠞⠋⠁⠀⠀⠀ ⡷⢿⡀⠀⠉⠳⣄⠀⠈⠛⠷⠀⠈⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⣼⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⢽⡦⠄⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⠦⣀⣀⣀⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠖⠋⠉⠙⠓⠦⣄⣀⠴⠒⢉⣉⣉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣼⣵⣒⠭⠭⠤⠤⣝⡆⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⣀⠴⣾⡟⠉⠉⢍⠀⠀⢉⣿⣿⠿⠗⠐⠒⠒⠠⣄⡉⠆⠀⠀⠘⣄⠀⠀⠀⠀ ⡾⠁⠠⠤⠬⠷⢦⣌⣃⣰⠟⠉⠀⠀⢀⡀⡀⠀⠀⠀⠉⠳⡄⠀⠀⢸⡦⡀⠀⠀ ⠉⠉⠉⠉⠁⢿⣿⣽⡟⡟⠉⠉⠉⠉⠹⣿⣿⣿⠛⣗⣲⣶⡧⠖⠂⠀⠇⠈⢂⠀ ⣶⣒⡒⠒⠶⠤⠿⢯⣦⣿⣶⠖⠲⠶⠶⠾⠿⢛⣋⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⢂ ⠁⠙⢯⣄⡀⠀⠀⢀⣼⠁⠉⠳⢖⡒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⣴⡞⠁⠉⠉⠛⠉⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡟⢦⣄⣀⣀⣀⣀⣀⣀⣀⣠⢤⢤⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣃⣛⣛⣿⣿⣿⣻⣿⣿⡶⠾⠿⣿⠿⠛⠉⣹⠋⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⡷⣼⡟⠀⠳⡀⠀⢀⠴⠊⡁⠀⣠⠞⠁⠀⠀⠒⠋⠁⠀⠀⠀⢀⣠⣴ ⠀⠀⠀⠀⠀⠉⢷⠂⠀⠙⠚⠁⠀⢀⣴⣞⡀⢀⣀⢀⣀⡀⣤⣤⣔⣒⡽⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠈⢀⡼⠷⣿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠙⢦⣀⠀⠀⠀⠀⠀⠀⢤⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⢀⣾⣿⣿⣿⣿⣾⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠃⠀⠀⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢹⣿⡆⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡟⢦⣀⡀⠀⠀⢀⣄⣀⣀⣠⣠⣤⣤⣴⣶⣦⣄⠠ ⠀⠀⢠⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠉⠈⠙⣿⣧ ⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟ ⠀⣾⣿⣿⠀⠀⠀⢰⣾⣦⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⡯⠜ ⡀⣿⣿⡟⠀⠀⠀⠈⠛⠁⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⢻⣿⣻⣿⠿⠟⠛⠉⠀⠀ ⣗⣿⢿⣿⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⡛⣧⠀⢹⡆⠀⠀⠀⠛⠋⠉⣙⠛⢷⣄⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠈⠿⠶⠖⠒⠒⠛⠋⠉⣷⠀⠁⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⢶⣶⡶⠛⠁⠀⠀⢀⣀⣠⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣬⣷⣄⣀⣀⣀⣀⣠⣿⡿⠋⠙⠛⠋⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠛⠋⠉⠉⠉⠈⠉⠉⠙⠚⠫⢖⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⡷⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠿⣿⡿⠃⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢷⠀ ⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣧⠀⠀⣴⡶⢶⣦⡀⠀⠰⣿⡿⠿⠿⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⣿⡅⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⣿⡇⠀⠘⣿⣤⣤⣤⣤⣴⣶⣶⠶⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⢰⡿⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠙⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠟ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣀⣀⣀⣠⣄⣤⣤⡴⠶⠾⠛⠉⠀⠀⠀ ⠀⠈⢿⣻⣆⡀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠋⣽⣿⣿⣶⣾⣷⣿⣛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀ ⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠤⣤⠞⠋⠁⠀⠀⢳⡀ ⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⡾⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⣸⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⡆ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠘⢧⠀⠀⠀⠀⠀⣀⣀⠀⠖⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠈⠳⢤⣀⣠⠞⠉⢨⣇⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⠀⠀⠉⡟⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⡼⠉⠛⠓⠒⠶⠶⠶⠶⠒⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠄⢀⠴⠋⣽⠟⣽⣿⡶⠔⠒⠒⢶⣆⣩⣽⡶⠛⠉⠣⡕⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⡿⠁⠸⠋⠁⠀⠀⣠⣄⡀⠹⡿⠋⣀⡀⠀⠀⠹⡞⠀⠀⠀⠀ ⠀⠀⠐⣰⠋⢹⠟⠀⠀⠀⢀⡀⠀⣰⠏⠈⠻⣆⢀⡾⠻⣷⠀⢰⡀⣿⠀⠀⠀⠀ ⠀⣰⣀⡿⢀⡏⠀⠀⣠⣶⣿⠛⠀⣏⣠⡴⠒⠚⠛⠒⠢⣌⣧⢸⠁⠘⢦⢢⠀⠀ ⣰⣿⣿⢿⣿⠁⢀⣼⠟⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⣮⠳⣕⠄ ⢿⣿⠏⢸⡏⢀⡞⠁⣤⣀⠀⡴⠃⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣷⣤⡾⠚⣷⠘⣆ ⢸⡟⠀⢸⠇⡞⠀⠀⠈⣹⠟⣛⣳⣶⣖⣛⡋⠀⠀⠀⠙⣳⣟⣿⣭⣆⠀⢻⣇⢻ ⢸⡇⠀⣾⠀⠀⠀⢀⣾⣷⠿⠟⣿⣉⣉⣹⠋⠀⠀⠀⠿⢿⣏⣉⣹⣿⡷⢨⡟⣞ ⠀⣧⢠⣿⡄⢇⠘⢹⠻⢄⣀⠤⠼⠿⠿⠯⠀⠀⠀⠀⠀⠈⠿⢿⣟⡋⠀⢸⢀⠃ ⠖⣽⣿⣿⢱⠘⢆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣸⡌⠀ ⡶⣻⡙⠘⢿⡰⠀⢳⢵⡀⠀⠀⠀⢀⣀⣤⣤⡴⢶⣦⢴⣤⣤⣀⠀⢠⣿⡿⠇⠀ ⠀⠣⡷⣤⣼⡟⢦⡘⣆⠉⠀⠀⠀⠀⠉⠁⠀⣠⠞⢀⠎⢸⡄⢻⣤⡾⢿⡼⡀⠀ ⠀⠀⠈⠙⣿⢁⢢⡉⠻⡷⢤⣀⣀⠀⠀⢀⣼⠃⢠⠋⢠⠋⣷⠈⡏⠀⠀⢷⠁⠀ ⠀⠀⠀⣰⢿⢸⡄⠙⠄⢹⡛⢿⡉⠛⢻⣿⠇⠐⠃⣠⠋⢀⡇⠀⣿⢦⢰⢸⢸⠀ ⠀⢠⠞⠁⠀⠻⠘⢦⠀⢸⠀⠀⠻⣶⣟⢈⠄⠀⠀⠁⠀⡼⠀⠀⡿⠯⣷⢟⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢞⣭⡴⠒⠀⠒⣢⣬⠤⠀⠐⠒⠒⠒⠺⠦⠤⠬⣭⣿⣛⣛⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⣫⡿⠿⡞⢁⣠⡶⠖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⣮⣍⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠚⠁⠀⣠⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⢀⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠞⠉⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣆⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠹⣷⢿⡀⠀⠀⠀⠀ ⠀⠀⣷⣿⣿⠇⠀⠀⠀⠀⡼⠁⢀⡼⣫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣆⢳⡀⠀⠀⠀ ⠀⢠⣟⣽⡇⠀⠀⠀⠀⣼⠁⠀⣨⡾⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢻⡟⣧⠀⠀⠀ ⣸⣿⣿⣿⠁⠀⠀⠀⢰⣇⡤⠞⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠘⣧⢹⡆⠀⠀ ⣿⣿⡾⠃⠀⠀⠀⠀⣿⢉⣀⣀⣤⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠈⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠄⠀⠀⢿⢸⡇⠀⠀ ⣿⡋⠀⠀⠀⠀⠀⠀⡿⠛⣻⣿⣿⣿⣶⣾⣿⡀⠀⠀⣾⣄⢠⣟⠀⠀⣀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢸⠀⡇⠀⠀ ⣿⡙⢶⣤⣄⠀⠀⠀⣇⠀⡿⠟⣿⡿⠿⡿⠀⠙⠦⣄⣡⠈⠛⢻⣿⣶⣿⣷⣦⣄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢸⡆⠃⠀⠀ ⠀⠉⠳⣦⣽⣷⣄⠀⠹⡆⣷⠐⠟⠓⣼⠃⠀⠀⠀⠀⠉⠀⢠⣿⠛⣿⣿⣾⣿⡟⣿⠟⢷⠁⠀⠀⠀⠀⠀⠀⣤⠀⣀⣴⠞⠉⡀⠀⠀⠀ ⠀⠀⢰⡿⣸⠏⠸⡟⠉⠁⠙⠧⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠻⡅⢀⡿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠀⠀⠀⠸⣆⡑⠄ ⠀⠀⢸⢁⡏⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡤⠞⠀⠀⢀⡾⠁⠀⣀⣤⠴⠃⣠⢾⣟⣀⣀⣀⣀⣀⣀⣈⠻⢀ ⠀⠀⡎⢸⡇⠀⢳⡈⢦⡀⠀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⣼⣅⠀⠀⣨⡵⢏⠀⠈⠉⠛⢿⣿⠭⣥⣶⠿ ⠀⠀⡇⣾⡇⠀⠘⡇⠀⢹⠟⠁⠀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡙⡛⠛⡛⣯⠀⠀⠳⣤⣤⣤⣤⣌⠿⢸⡇⠁ ⠀⠀⡇⣿⡇⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠁⠁⠁⠉⠁⢻⡄⠀⠀⠈⢷⣟⢦⣤⡴⠛⠁⠀ ⠀⠀⢳⢸⡇⠀⠀⠀⢸⡿⠲⣤⣄⣀⣀⣿⣿⠶⠶⣶⠦⣤⣤⠴⣶⣶⠶⣒⡋⢉⡿⠀⠀⠀⢀⠀⠀⣸⣿⣦⡀⠀⠀⠙⢶⣍⠳⢤⠀⠀ ⠀⠀⠸⣧⢻⡄⠀⠀⣼⡧⠀⠀⠈⠉⣹⣿⣿⠋⠉⢻⣤⣶⠶⠚⠋⠉⠉⠙⣿⡟⠁⠀⠀⣠⡟⠀⠀⣿⣿⡿⣯⣛⡲⠶⢶⣬⣿⢸⠀⠀ ⠀⠀⠀⠘⢯⣻⣦⣠⠟⠀⠀⠀⠀⠀⣿⢁⣹⣤⡞⣋⣁⣠⡴⠶⠛⠛⠉⠙⣿⣤⣤⣤⠾⠉⠀⠀⢠⣿⣼⠃⠀⠀⠉⠉⠛⠛⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢀⡿⠻⣇⠀⠀⠀⠛⠛⠳⣄⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⣠⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡾⣧⡀⠀⠠⠴⠛⢙⡀⠀⠈⠓⢦⡀⠀⠀⠀⠈⢳⡄⠀⣠⣾⣃⣀⣀⠤⠶⣿⡿⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣎⡻⠶⠤⠴⣾⡿⢧⡀⠀⢤⣄⣻⡄⠀⠀⠀⠈⣷⠉⠛⠦⣌⣀⠀⠐⠺⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢛⡛⢓⣾⣉⢡⣤⣿⣷⣿⣭⡭⠽⠟⠛⠛⢻⣿⣦⣤⣤⣤⣬⡟⣓⣐⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣷⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⢷⣶⣦⣤⣤⣀⠀⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟ ⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠛⠉⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇ ⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠉⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⢀⣾⡟⠁⠀⠀⠀⢼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢳⣌⢌⡻⢿⣷⡀⠀⣀⣤⣾⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣻⢿⣿⣿⣷⣿⣿⢿⡿⣿⣷⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠈⠳⣃⠌⣹⣷⣾⢿⣻⡽⣾⣿⣟⡷⣿⣿⣿⢿⣟⢯⣷⣹⢾⣹⢳⣟⣿⣿⣿⣿⣿⣟⡟⣾⢏⣿⢳⡿⣿⣜⣧⡀⠀⠀⠀⠀⠀⠀ ⣀⠠⠇⠀⠈⣿⡿⣽⣫⣟⣶⣿⣿⣻⣜⣿⣟⠿⣼⣫⣞⢯⡶⣫⣷⣯⣷⢺⣭⢿⣿⣟⢧⣻⢾⣭⡟⣾⣫⢷⣻⣿⣎⠳⠀⠀⠀⠀⠀⠀ ⠀⠉⣇⠀⣼⣿⣽⣿⣿⣿⣿⣿⣟⢶⡻⣮⢽⡻⢧⢷⣫⢷⣹⣿⣿⢿⣿⣿⣼⢫⣟⢮⣿⣿⣿⣷⣿⣱⢿⣧⢷⣻⣿⡆⠀⠀⠀⠀⠀⠀ ⢀⣀⣈⣾⣟⣾⣿⣳⣯⣿⢯⣟⢾⣫⢷⡭⣷⣻⣿⣎⢷⣫⣿⣿⢯⣟⡾⣽⢿⣷⣮⣿⢿⣯⢿⣿⣷⢯⣻⣿⣧⢯⣿⡧⡇⠀⠀⠀⠀⠀ ⡄⠀⣼⣟⡾⣿⣯⣿⢿⣯⣟⢾⣫⢷⣫⣾⣿⣿⣿⢿⡾⣿⡿⣽⢫⣾⡿⢾⣯⣿⠿⣿⣯⣾⣯⣟⣿⣯⣟⣿⢿⣳⢿⣧⡙⣦⠀⠀⠀⠀ ⣟⣾⣿⣿⣿⣿⣿⣽⣿⣳⢯⡿⣱⣿⣿⣿⣟⣿⣯⢿⣻⣽⣿⠾⢛⠛⠙⠃⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⣾⣿⣏⠿⣞⣽⣿⣎⡳⣄⠀⠀ ⣿⣿⣿⣿⣿⡿⣿⣿⣯⣟⣯⣽⣿⣿⣟⡷⣻⣟⡾⣏⢷⣿⠡⠎⠄⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⢿⣿⡾⣭⡟⡽⣾⣯⢿⣷⡝⢷⡀ ⣿⣿⣿⣿⡿⣽⣿⣿⠾⣵⣻⣿⣟⡷⣫⡽⣟⡾⣹⢮⣿⢃⠱⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠠⠐⠂⣿⣟⣧⢻⣵⣯⣿⣿⣞⣿⣦⠃ ⣿⣿⣿⡿⣽⣳⣿⣯⢟⣷⣿⡻⡼⣿⣷⣿⣵⣫⣷⡟⢡⠊⠀⠀⠀⢀⣠⣶⣦⠀⠀⠀⠀⣤⣄⠀⠀⠀⣼⣿⣾⣿⣿⢳⣻⣿⣿⡞⣿⣧ ⣿⣿⣿⣻⡵⣫⣿⢧⣻⣿⢣⡟⣵⢫⡝⣻⣿⡿⣿⣿⣿⣶⣶⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣟⣵⣯⠶⡭⣿⣿⣿⣹⣿ ⣻⣿⡿⣵⢫⣽⣿⢣⡿⢧⡻⢼⣩⠗⣼⣿⣟⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⡳⢽⣿⣿⣳⣿ ⣿⣿⣿⢭⡗⣾⣿⣹⣏⠷⣍⡳⣌⣿⣿⣿⣿⣿⠿⠿⣿⡏⢉⣁⣈⣩⣿⠏⠀⠀⠀⠀⠀⣿⣿⠿⣿⣉⣀⣤⣴⣿⣿⣿⣿⢩⣿⡟⣿⣿ ⠃⢿⣿⢮⣝⣿⡿⣜⣿⣙⠦⣿⣿⣿⣿⡉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⠟⣰⢫⣿⠱⢻⣏ ⠀⣸⣿⡗⣾⣿⣿⣎⢿⣯⢚⡱⢺⡟⢛⢧⣠⣤⣶⡶⢶⠿⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⣠⠤⡼⠿⢿⣿⣿⣵⣮⡙⢦⢻⣯⢼⡈⣁ ⣴⣟⣿⣿⣻⣿⣟⣿⣎⢿⣧⠎⣽⡏⡌⠭⡉⠀⠀⢀⡀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⡈⠙⢿⣿⣌⠿⣿⡰⠁⠀ ⣉⣿⣿⢿⣿⠿⣿⣿⣻⣮⢟⣿⣜⣿⡔⢡⠃⠀⣉⠲⢌⡋⡔⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠊⡴⢡⡃⠸⣿⣿⣯⣿⡇⠀⠀ ⣿⡏⣿⣏⠿⣃⠿⣿⣷⣻⣟⡞⣿⣿⣿⣄⠣⡐⠠⠉⠆⠱⢈⣂⣴⣤⣶⣶⣶⣷⣷⣾⣶⣶⣷⣦⣤⣤⣁⡀⠁⠂⢀⣿⣿⣿⢿⡇⠀⠀ ⠏⠹⣟⣿⣦⠀⠀⣿⣿⣷⣯⣻⣽⣇⠻⢿⠆⠁⠆⠀⠈⠀⠘⢿⠿⠟⠛⠋⠙⢉⣽⡿⢋⢭⡿⠻⣿⡙⢿⣷⡀⠀⣼⣿⣯⢻⡎⠁⠀⠀ ⠀⠀⠹⠿⣿⢿⣦⣿⣿⣻⢿⣷⣯⣿⣆⠢⠌⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢀⣳⡿⠁⢠⣿⡇⡜⣿⣧⣿⣿⢿⣿⣷⢻⡄⠀⠀ ⠀⠀⠀⠀⠉⠛⡿⣿⣿⣻⣿⣽⣻⣿⣿⣿⣮⣔⡠⢁⠂⠄⠀⠀⠀⠀⢀⣼⣿⠏⢠⣿⠏⠀⣰⡿⢙⣿⢠⢸⣿⡿⣽⣛⡾⣿⣏⢃⠀⠀ ⠀⠀⠀⠀⠀⠈⣼⣿⣟⣷⣻⢿⣷⡽⣻⣷⣍⣻⣿⣿⣶⣮⣖⣳⣄⣠⣾⣿⠃⣰⣿⠃⢀⢼⡿⠁⢠⣿⢌⢸⣿⣿⡱⣯⣝⣻⣿⢰⡀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣽⣿⣯⣛⠾⣿⣱⣻⣿⠻⣿⣿⡈⡝⢛⠛⣿⣿⣿⠃⠈⠋⠉⢠⢮⡿⠁⠀⢸⡏⠤⢘⣿⡿⣷⣣⣿⡜⣿⣼⡁⠀ ⠀⠀⠀⢠⣾⠿⠉⠞⣿⣿⡻⣯⣏⡗⣧⢳⣿⡗⢌⠻⣿⣶⣭⣼⣿⢹⡏⠀⠀⠀⠀⠽⠛⠀⠀⢀⣿⢏⠂⢹⣿⣷⣾⣿⣹⣿⣟⡯⠀⠀ ⠀⠀⣰⣿⠋⠀⠀⠀⠉⠻⣇⠹⣿⣞⡼⣻⣿⡁⠀⠁⠙⣿⣿⣿⣿⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⣾⡟⢢⠁⢸⣗⣻⠻⢩⣿⡿⣽⡃⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡬⠟⠛⠉⠙⠛⠫⢴⣀⣀⠀⠰⠒⠛⠻⢧⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⣠⠴⠒⠂⠐⠒⠢⢽⣧⠀⠀⠀⢀⡀⠀⢈⣙⣦⡀⠀⠀⠀ ⠀⠀⣠⡿⠃⢀⡴⠋⢀⡠⠖⠊⠉⠉⠉⠓⠿⣏⠉⢀⡤⠖⠒⠒⠛⠿⢿⣷⣀⡀ ⠀⣠⣿⢁⢶⠋⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⢈⠻⣟ ⣾⠟⡇⢸⣸⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈ ⣿⠀⠁⠀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢠ ⢸⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠈⣋⣤⣧⣀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⢖⡫⠟⠋⠁⢈⡙⠒⠂⠐⠒⠊⣩⣼⡟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠻⣾⡀⠘ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣰⠀ ⠀⠀⠀⠀⠀⠠⡞⠁⠐⠢⠤⢤⣬⣍⣉⠙⠒⠒⠲⠶⠦⠤⠶⠖⠛⢋⣩⣼⣿⢷ ⠀⠀⠀⠀⠀⣄⠙⠒⠒⠒⠒⠶⠤⣤⣬⣭⣉⣉⣉⡁⠐⠂⠐⠀⢙⡿⠋⠀⣼⣿ ⣄⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢿⣅⡀⠉⠙⠛⠿⣭⣉⣩⣿⣿⡇⠀⠐⣇⠀ ⠟⠿⢭⣟⣒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣈⣉⡓⠶⣦⡄⠀⠈⠉⠛⠻⠗⠀⠀⠙⢾ ⠀⠀⠀⠀⠉⠉⠛⠚⠒⠶⠶⠶⠦⠤⠶⠖⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀
🫧 𝐈 𝐜𝐨𝐦𝐞 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐦𝐚𝐤𝐞 𝐜𝐮𝐭𝐞 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬/𝐞𝐦𝐨𝐣𝐢 𝐜𝐨𝐦𝐛𝐨𝐬 𝐟𝐨𝐫 𝐩𝐞𝐨𝐩𝐥𝐞, 𝐛𝐮𝐭 𝐚𝐟𝐭𝐞𝐫 𝐰𝐡𝐚𝐭 𝐢'𝐦 𝐫𝐞𝐚𝐝𝐢𝐧𝐠 𝐚𝐧𝐝 𝐬𝐞𝐞𝐢𝐧𝐠 𝐈 𝐦𝐢𝐠𝐡𝐭 𝐬𝐭𝐨𝐩 𝐛𝐞𝐜𝐚𝐮𝐬𝐞 𝐭𝐡𝐢𝐬 𝐢𝐬 𝐬𝐮𝐩𝐩𝐨𝐬𝐞𝐝 𝐭𝐨 𝐛𝐞 𝐚 𝐰𝐞𝐛𝐬𝐢𝐭𝐞 𝐟𝐨𝐫 𝐩𝐞𝐨𝐩𝐥𝐞 𝐧𝐨𝐭 𝐟𝐨𝐫 𝐩𝐞𝐨𝐩𝐥𝐞 𝐭𝐨 𝐛𝐞 𝐚𝐫𝐠𝐮𝐢𝐧𝐠, 𝐛𝐞𝐢𝐧𝐠 𝐬𝐭𝐮𝐩𝐢𝐝, 𝐚𝐧𝐝 𝐦𝐚𝐤𝐢𝐧𝐠 𝐬𝐢𝐥𝐥𝐲 𝐢𝐧𝐚𝐩𝐩𝐫𝐨𝐩𝐫𝐢𝐚𝐭𝐞 𝐭𝐡𝐢𝐧𝐠𝐬.🌷
reas̷̫̬̗͑͆o̷̢̨̧̯̭̭̰͚̞͓̠̜͒̊̀̇̍̓̓̊́͜͠n̸̝̫̂͗̂̒̈́̂͒̚
Friday 21 September 2007 Scripture, Tradition, Reason, Experience I have been musing on the four guides that we ought to trust in making sense of the world we live in. Relying on any one of these to the exclusion of the others is not a good idea. The best way to discover the truth about reality, and more importantly to discover how to behave as a result of knowing that truth, is to take seriously all four guides. SCRIPTURE. As a Christian, I believe that God speaks in and through the written text of the Bible, and therefore the Bible is a book I should trust. This is not to say I should take everything in it as the literal truth. There are layers of meaning (as with any text) and the most important truths are not always on the surface. The Bible is a book to engage with – to absorb, study, question, wrestle with, listen to and above all take seriously. John Campbell, in “Being Biblical”, has some very interesting things to say about the way we approach Scripture. TRADITION. Why reinvent the wheel? Better brains than mine have tackled the same issues as I face today. Admittedly some of them lived long ago and in different cultural contexts, and their conclusions are not always valid for my own age and context. But it is still worth knowing what others think. Truth is best discovered in a community setting, listening to and sharing with others, taking seriously the voices of the past as well as the present. REASON. I like to think of myself as a rational creature. I am not interested in a stupid faith. My understanding of the world has to be a sensible one. Careful thought, logical examination of the evidence, honest common sense – all of these are vital if I want to get to the truth. EXPERIENCE. Does my view of the world match personal experience? If not, there is something sadly wrong. In fact my own unique experience of life, in physical, mental and spiritual terms, is the raw material from which I derive my understanding of life. Where’s the point in trying to establish the truth based purely on thought-experiments or abstract principles? Truth is to be found in the material, emotional and spiritual roller-coaster of day to day life. As I said, we must trust each of these guides. Anything which is fundamentally at odds with one or more of them is something to be very wary of. An interesting aside: A few years ago a group of local ministers were debating this topic over one of our fellowship lunches. All agreed that we need to respect scripture, tradition, reason and personal experience, but there were differences of opinion as to which of these should be given higher priority. The evangelical ministers favoured the Bible and the high church ministers regarded tradition as important. After the meeting I realised that the entire discussion had been conducted on the basis of reason. We did not get out our Bibles and compare texts. We did not quote the wise pronouncements of the church. We did not each insist that we were right because of our own personal experience. We acted as if the truth could be discovered by reason and we debated it in friendly and logical fashion. From that I conclude that to all intents and purposes we live in an age where reason is seen as having higher priority than scripture or tradition – though in a post-modern world personal experience is increasingly becoming the yardstick by which ‘truth’ is measured. mathmethman at 11:26
Just me or is there more gossip than emojis? Oh btw, a guy i know showed up to the store in like, a crop top. like, girly pink sequined crop top. reason? because he quote "Wanted to show off his abs" 🙄😒
can yall stop submitting “free palestine” “free ukraine” free blah blah like ppl r here for cute symbols not 4 sum free free free blah blah, also i support them but just let people use this website normally 😭 ᡣ𐭩 ᡣ𐭩 ᥫ᭡。 ᥫ᭡。 ᶻ 𝘇 𐰁 ᶻ 𝘇 𐰁 ᶻ 𝘇 𐰁
⣿⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡏⢇⠀⠀⢸⡄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠸⡄⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡸⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⢳⠀⠈⣷⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡇⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠘⡄⠠⡿⠦⠐⠒⠒⠛⠛⠿⠤⢀⣰⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠁⣀⡠⠽⠿⠿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⣴⣶⣿⣿⣿⣿⡂⠀⠀⠀ ⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣼⣿⣿⣿⣿⡷⢃⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠙⠻⣿⣿⡟⠁⠀⡸⣿⣷⡆⠀⠀⢀⡤⠖⠉⢹⣶⣶⣤⡀⠀⠀⢻⣿⣿⡇⠀⠀⠀ ⠏⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⡆⢀⠀⠀⠀⠘⣿⡀⠉⠀⠻⢿⣿⣿⠀⠀⡞⠀⠀⢀⣿⣿⣿⣿⣿⣆⠄⢸⣿⣿⡇⠀⠀⠀ ⣦⣔⣒⣊⣢⣄⣀⣀⡀⠀⠀⠀⢫⢆⠀⠀⢇⠀⠈⠢⠤⠖⣿⣧⠀⣀⠀⠈⠘⠹⠀⢸⠠⠔⠐⠈⠉⠉⠉⠉⠙⠷⠁⣼⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠉⢳⣀⠀⠀⠀⣹⣶⣿⡯⢄⠀⠀⠀⠀⠈⢯⣣⣧⡉⠒⠢⠤⢄⢀⣀⣀⣀⠠⠤⠤⠒⢪⠁⢀⣰⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠄⣼⣿⣿⣶⣾⣿⣿⣿⠷⠊⠀⠀⠀⠀⠀⠀⣱⡝⠻⣦⣀⠀⠀⡀⠀⠀⠸⠀⠀⠀⣠⠎⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡻⠋⠃⠀⠄⢀⣀⣀⠤⠔⠒⠋⠱⣿⣶⣿⠟⠋⠓⠒⣂⣤⣤⣶⡶⠛⠂⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠿⢏⠕⠚⡇⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⢀⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⡿⠿⢛⡉⠁⠀⠀⠘⠤⠐⢱⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⣽⡋⣙⢿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠐⠒⠈⠁⠀⣀⡼⠛⢿⣆⠙⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠘⠦⠤⠔⠂⠉⠀⠀⢀⣀⣀⡀⠤⠴⠒⠉⠁⠀⠀⠀⠈⠷⣌⢻⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡜⠉⠉⡆⣠⠔⠒⠉⠁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⢧⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⠀⠉⠸⢄⣤⣶⣿⣿⣿⣿⣿⣿⡏⠈⠉⠉⢩⠉⢩⣿⣿⣦⣀⠀⠀⠀⠑⢦⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠛⠛⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⡄⠀⢠⣿⣿⣿⣿⣧⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣗⠀⠀⡌ ⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠟⠁⠈⠀⠒⠠⠄⣈⠙⠿⣇⠀⢀⠆⠄⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⡼⠀ ⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⠑⠢⣉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠙⢦⡀⠀⠀⠙⢿⣿⣿⣿⣞⢵⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡤⠤⠀⠒⠀⠤⢀⠀⠀⠀⢱⣤⠄⠬⣿⣿⣿⣿⣿⣷⠀⢸⣿⣦⡀⠀⠀⠙⢿⣿⣿⠀⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡃⠄⠀⠈⢻⠿⠿⠿⠛⠒⠚⠛⠛⠛⠁⠁⠒⠀⣿⠿⠀⠀ ⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠛⢄⣀⠠⠤⠒⠓⠂⢄⠀⠀⠀⠀⠀⠀⠸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⠿⠟⠓⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⡸⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
at this point there is more ppl talking abt the beef than the beef… 💀
all yall sum BlTCHES 💀
⨺⃝⨺⃝ 🪶🌿🍃𓃹ㅤ/ᐠ - ˕ -マ𓃮🪶ВE WILD-⃝⃤₊˚✧𑁍.ೃ࿔*Live This new life the best you can♡・ love yourself:)🩷
ᖭི༏ᖫྀʚïɞ✧you are beautiful no matter what!˖°ʚïɞᖭི༏ᖫྀ✧˖°
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢋⣉⣀⣠⣄⣀⣈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⠴⠚⠉⠉⠀⠀⠀⠀⣤⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⢛⠁⠁⣸⠀⠀⠀⠀⠀⣤⣾⠵⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⣠⠀⡇⢧⠀⠀⢀⣠⡾⡇⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠘⣿⠀⣀⡠⠞⠛⠁⠂⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣻⡦⣞⡿⣷⠸⣄⣡⢾⡿⠁⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠐⠠⡤⣾⣙⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡷⠰⣔⣾⣖⣾⡷⢿⣐⣀⣀⣤⢾⣋⠁⠀⠀⠀⣀⢀⣀⣀⣀⣀⠀⢀⢿⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡦⠴⠴⠤⠦⠤⠤⠤⠤⠤⠴⠶⢾⣽⣙⠒⢺⣿⣿⣿⣿⢾⠶⣧⡼⢏⠑⠚⠋⠉⠉⡉⡉⠉⠉⠹⠈⠁⠉⠀⠨⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠐⠀⠀⠀⠈⣇⡿⢯⢻⣟⣇⣷⣞⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣆⠀⠀⠀⠀⢠⡷⡛⣛⣼⣿⠟⠙⣧⠅⡄⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢶⠏⠉⠀⠀⠀⠀⠀⠿⢠⣴⡟⡗⡾⡒⠖⠉⠏⠁⠀⠀⠀⠀⣀⢀⣠⣧⣀⣀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣷⢿⠋⠁⣿⡏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢏⡵⠛⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠀⠀⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⠛⣲⡏⠁⠀⠀⠀⠀⠀⢀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⢾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠟⠀⢰⡯⠄⠀⠀⠀⠀⣠⢴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠁⠁⠀⠘⠧⠤⢤⣤⠶⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠂⢀⣀⣀⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⢀⣠⠞⠋⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⠻⣦⡀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⢠⡿⠁⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠈⢻⣄⠀⠀⠻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠏⠀⠀⢠⡟⠀⣠⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⣄⠀⢻⣆⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⢰⣿⣇⣰⠋⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠘⣧⣼⣿⣆⠀⠀⠹⣧⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⢰⣿⣿⣿⡇⢠⡟⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠸⣏⡀⠀⠀⠸⡆⢸⣿⣿⣿⣇⠀⠀⠹⣇⠀⠀ ⠀⢠⡟⠀⠀⢰⡾⠈⣿⣿⣧⣿⢀⡶⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢶⡀⢿⣼⣿⣿⠙⢿⡆⠀⠀⢻⡆⠀ ⠀⣾⠁⠀⢠⣼⠃⠀⣸⢏⣿⣧⣼⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣧⣼⣿⡿⣏⠀⠘⣧⡄⠀⠈⣷⠀ ⢰⡏⠀⠀⢸⡟⠀⢠⡟⠘⠿⢻⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠃⢹⡄⠀⢹⡇⠀⠀⢹⡇ ⢸⡇⠀⠀⣸⡇⠀⣾⠁⢀⡏⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⢸⡄⠈⣷⡀⢸⣧⠀⠀⠸⡇ ⢸⠀⠀⢀⡟⠻⣾⣿⡀⣸⠃⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠈⣧⠀⣿⣷⡟⢻⡀⠀⠀⡇ ⢸⠃⠀⢸⣇⣾⢹⡟⣿⣿⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣿⣿⢹⣇⣿⣼⡏⠀⠀⡇ ⢸⠀⠀⢸⣿⠏⣽⢸⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣇⣿⠽⣿⣧⠀⠀⡇ ⢸⡆⠀⣼⠁⠀⡏⠘⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢸⠀⠈⣷⠀⢰⡇ ⠸⣷⠀⢻⠀⢰⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⢸⡇⠀⡟⠀⣾⠇ ⠀⢿⡄⢸⠀⣼⡧⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣸⣧⡀⡇⢠⣿⠀ ⠀⠸⣇⢸⣾⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡇⣸⠇⠀ ⠀⠀⢻⣼⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢾⢧⡿⠀⠀ ⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠓⠒⠤⣰⠋⠹⡄⠀⣠⠞⣿⠀⠀ ⠀⠀⠀⢀⠄⠂⠙⢦⡀⠐⠨⣆⠁⣷⣮⠖⠋⠉⠁⠀ ⠀⠀⡰⠁⠀⠮⠇⠀⣩⠶⠒⠾⣿⡯⡋⠩⡓⢦⣀⡀ ⠀⡰⢰⡹⠀⠀⠲⣾⣁⣀⣤⠞⢧⡈⢊⢲⠶⠶⠛⠁ ⢀⠃⠀⠀⠀⣌⡅⠀⢀⡀⠀⠀⣈⠻⠦⣤⣿⡀⠀⠀ ⠸⣎⠇⠀⠀⡠⡄⠀⠷⠎⠀⠐⡶⠁⠀⠀⣟⡇⠀⠀ ⡇⠀⡠⣄⠀⠷⠃⠀⠀⡤⠄⠀⠀⣔⡰⠀⢩⠇⠀⠀ ⡇⠀⠻⠋⠀⢀⠤⠀⠈⠛⠁⠀⢀⠉⠁⣠⠏⠀⠀⠀ ⣷⢰⢢⠀⠀⠘⠚⠀⢰⣂⠆⠰⢥⡡⠞⠁⠀⠀⠀⠀ ⠸⣎⠋⢠⢢⠀⢠⢀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⣬⣅⣀⣬⡷⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⢲⠋⠁⠀⠘⡷⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡴⠒⠢⡄⠀⠀ ⠀⠀⠀⠀⣠⠋⠁⠀⠙⢾⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠱⡜⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠈⢣⠀⢀⠖⠉⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣄⠀⠀⠀⠀⠈⠳⢄⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⡀⣀⡔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠖⠒⢼⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡼⠀⠀⠀⠀⡾⠋⠉⠛⠳⣄⣴⠃⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢾⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠳⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣲⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠚⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⢠⣤⣶⣾⣧⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠴⠶⠤⢤⡀⣧⣀⣀⠀ ⠻⠶⣾⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢹⣿⣭⣽⠇ ⠀⠀⠙⠤⠴⢤⡤⠤⠤⠋⠉⠉⠉⠉⠉⠉⠉⠳⠖⠦⠤⠶⠦⠞⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⢧⣀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠏⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⢙⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣒⣶⠦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠲⡌⠙⢦⠈⢧⠀ ⠀⠀⠀⣠⢴⡾⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢃⡠⠋⣠⠋⠀ ⠐⠀⠞⣱⠋⢰⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣋⡥⢖⣫⠔⠋⠀⠀⠀ ⠈⠠⡀⠹⢤⣈⣙⠚⠶⠤⠤⠤⠴⠶⣒⣒⣚⣩⠭⢵⣒⣻⠭⢖⠏⠁⢀⣀⠀⠀⠀⠀ ⠠⠀⠈⠓⠒⠦⠭⠭⠭⣭⠭⠭⠭⠭⠿⠓⠒⠛⠉⠉⠀⠀⣠⠏⠀⠀⠘⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠁⣰⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠉⢳⡞⠉⠀⠀⠀⠠⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⡆⢀⣼⠟⢳⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣧⡞⠁⡴⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣠⣿⡇⣾⢁⡞⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡶⠿⠛⢻⣿⣯⠍⠹⠑⢇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠶⠖⠚⠋⠉⠉⠀⢾⣿⣷⣦⢤⣿⣿⣛⡻⡦⠀⠈⠙⡆⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣘⣿⡗⠀⢯⢸⣿⠿⠂⠀⠀⠀⣿⡄⠀⠀⠀⠀ ⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀ ⠀⠀⠘⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⡄⠀⠀⠀⢻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢯⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠰⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⡀⠀⠀⠀⠀⠙⠿⠾⠛⠁⠀⠀⠀⣀⣾⣷⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⢷⣶⡶⠤⢤⣴⡤⣶⢶⣶⣶⣿⡿⠟⠉⠀⠙⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠋⠀⠀⢤⣴⠆⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⢀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡖⠛⠈⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠉⠀⠉⠀⣠⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢦⡟⠻⢿⣶⣶⢶⣦⣤⣤⣤⣤⣴⣾⡿⣿⣄⠀⠀⢀⣽⠃⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠳⣯⢻⣿⣿⡯⠭⠭⠯⠥⠀⢈⢻⡷⢶⢿⠧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠉⠛⠛⣿⡗⠒⠒⠃⠀⠀⠈⠳⠇⢸⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠙⢶⡦⠀⠀⣿⡆⠀⢰⣄⠀⠀⠀⠀⢸⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣧⣀⡀⠀⠀⠀⢸⣷⣀⠀⠋⠛⠀⠀⠀⢸⣸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠈⠉⠉⠉⠉⠉⢹⡏⠛⠲⠶⠶⠶⠶⠞⣯⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣶⣦⣤⣤⣤⣀⣀⣧⠀⢀⣀⣀⡀⠀⣠⣽⡿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠁⠀⠀⠀⠙⢏⣷⠛⠛⣍⣹⣿⣿⣻⣿⣿⡿⠿⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠃⠀⠀⠘⣿⣦⣶⡏⠁⠀⠀⠈⠻⣿⣧⣠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠛⣷⠄⠠⣀⡀⠠⠼⢿⣻⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠲⠖⠒⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠃ ⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀ ⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀ ⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡞⠀ ⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⢧⠀⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣷⣶⣶⣶⣤⣤⣀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠸⠀⠀⠀⠀⢸⡀⠀⢰⠃⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⣷⡀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⡇⠀⠀⠀⠈⡇⢠⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡇⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⡇⣼⣿⠟⠋⠉⠀⠀⠀⠀⠈⠉⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⠁⠀⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⢳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣶⣚⠋⢉⣁⡠⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⣟⣒⠤⠭⠡⠤⠴⠀⣠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣇⠀⢀⠳⡄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡤⠀⠀⠀⠙⠻⠖⡒⡊⠵⢺⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣹⡄⣈⠣⡈⠢⣌⠳⣄⠀⠀⠀⠀⠀⠀⢠⠃⣹⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠙⡌⢢⡘⠢⡈⠳⣤⡷⠀⠀⠀⣀⠔⢧⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⠈⢦⠹⡗⢌⡓⢌⢳⡀⠀⠈⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⠱⡘⣆⠉⠒⠽⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣠⡤⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣀⡤⠤⠤⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⠓⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⠃⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢬⡙⠀⠀⣰⠃⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⡇ ⠀⠰⡆⠀⣠⣄⠀⠙⠀⢰⠃⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⣠⠏⠀⠀⢀⡟⠀ ⠸⡇⢧⠀⢹⣿⣷⣄⠀⡼⠀⠸⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠠⠔⠚⠁⠀⠀⣠⠞⠀⠀ ⠀⠈⠀⠁⠀⣿⣿⣿⣷⣼⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⡠⠤⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢱⡇⡿⠳⣄⡀⠀⠀⠀⠙⠿⠿⠟⠁⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⡟⢸⢷⡇⠰⠄⣹⡓⢦⣤⣄⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⡇⠀⢸⡇⠀⠀⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣲⣿⣿⡇⠀⠘⣷⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣹⣿⣿⣷⠀⠀⢻⡀⠀⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣼⣿⣿⣿⡄⠀⠈⣧⠀⠀⢸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡇⣿⣿⣿⣿⣿⣿⣆⠀⢹⣆⠀⠘⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⠿⢻⣿⣿⣿⣿⣿⣿⣦⡈⢻⣆⠀⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠋⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⢿⣿⣿⣿⠙⢿⣿⣿⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⣤⡀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⣽⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢰⣶⣶⣶⡆⠀⠀⠀⢰⣶⣶⣶⡆⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠈⠉⠉⠉⠁⣶⣶⣶⠈⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⣸⠿⣏⣉⣉⣉⣹⡿⣇⡀⠀⢸⣛⡀⠀⠀⠀ ⠀⠀⠀⠈⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠍⠉⠉⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡁⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣦⣀⢀⠀ ⠀⠀⠀⢀⣼⠇⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣠⡴⢫⠇ ⣤⣖⠚⠉⠀⠀⠈⠉⢛⡲⢦⣤⣀⠀⠀⣸⠀⢀⡴⣾⠁⠀⢸⠀ ⣯⠉⠛⠶⣤⣀⡠⠾⠛⠁⠀⠀⠉⠛⢓⣩⠾⠋⠀⣿⠀⠀⢸⠀ ⣿⠀⠀⠀⠀⢯⠙⠳⢦⣤⣀⠀⢠⡴⠛⢱⣂⠀⠀⣿⠀⠀⢛⡄ ⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⣛⠉⠀⠀⢸⣿⣿⣷⣶⢀⣴⠟⠀ ⣿⣶⣤⡀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡛⠿⣿⣿⠟⠁⠀⠀ ⠹⣿⣿⣿⣷⣮⣄⡀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⢿⣿⣿⣿⣷⣦⣄⡻⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⡿⠓⠶⠾⠿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠖⠻⠷⡶⣮⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣚⡯⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⣀⣀⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠛⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠉⠁⠀⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣾⠿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⢀⣼⡧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⡒⠒⠶⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⠀⢀⣠⣼⡟⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⠀⠀⠀⠤⠖⠚⠉⠉⣀⡠⠤⠒⢲⡆⠁⢀⡴⢩⡿⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣴⠞⠋⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⢽⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⢀⣤⣾⣥⠤⠴⠛⠋⠉⠙⣆⠉⠢⡄ ⠀⠀⠀⠀⠀⣠⠟⠁⢠⡾⠋⠁⠀⠀⠀⣼⡇⠀⡀⠀⠀⠀⠀⠀⢰⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈ ⠀⠀⠀⠀⣴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠿⢛⣣⣄⣀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⣼⠇⢀⡟⠁⠀⠀⠀⠀⠀⠀⠰⣿⠀⠈⠈⢻⣟⠉⠉⠉⠉⠉⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢠⣶⠏⢸⠛⠛⠒⢲⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣀⢀⣀⣤⣄⠀⠀⠀⠀⣀⣀⣾⣿⣿⣄⣠⣏⠀⠀⠀⠺⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠘⣷⣤⢹⣄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣯⣤⣴⣦⣾⠷⣿⡋⠀⠀⠈⠉⢹⣿⣦⣿⠛⢷⣬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡏⠙⢿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡀⠀⠀⠈⢿⡷⣦⡀⠀⢸⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⣇⠘⡆⢳⣬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⢻⣶⠿⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⢷⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠳⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⢶⣄⣠⡴⠞⠛⠋⠉⠉⠉⠉⠉⠛⠒⠶⣯⡀⠀⠀⢀⣀⣈⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣴⠟⠉⠉⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣠⡾⠁ ⠀⢀⣤⣤⣤⣠⣄⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀ ⢠⡟⠁⠀⠀⠀⠈⠹⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠘⣧⡀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⠀⠿⠿⠟⠀⠀⢀⣤⠀⠀⠀⢴⣶⣶⠄⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠘⢿⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⡆⣀⣼⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀ ⠀⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠻⣦⡀⠀⠀⠀⠀⠁⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠈⠙⢧⡀⠀⠀⠀⠻⣦⡀⠀⠈⠛⠶⣤⣤⣀⣀⣤⡤⢤⣤⣄⣀⠀⠀⠀⣀⣠⡴⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠋⠛⠛⠛⠁⠀⠀⠀⣼⠋⢨⡟⠉⠂⠀⠀⠑⢬⠙⣿⠛⠛⢻⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡶⠶⠤⠤⠤⣼⠾⠿⠆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⣸⡇⢲⣶⣶⠒⣇⠀⠀⣀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠿⣦⣈⡉⠉⣀⣩⡿⠛⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠉⠉⠉⠉⢁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣤⠾⠛⠛⠛⠛⣿⠁⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⢦⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠐⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣯⣿⡋⠉⠹⣿⣯⣿⣿⡿ ⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⣤⣴⠶⣶⡒⠶⠒⣶⣾⣿⣿⣟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⣄⣀⣀⣀⣀⣼⣿⣿⣽⣟⣋⠉⢘⡷⣄⡀⡇⠈⠛⢯⣾ ⣿⡻⣯⡓⢿⣛⢦⣌⡓⢦⡀⠙⠳⢤⡙⢲⣾⣿⣿⣿⣿⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⣤⣀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢈⣴⣿⡇⠁⠀⠀⢸⢿ ⣄⠙⠚⢝⡦⡍⠓⢯⡛⢦⣍⠳⢤⡀⢉⣿⣫⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣇⡴⠂⠀⣸⡼ ⣿⡻⣦⣄⠉⠺⣽⣦⣌⠓⢮⡛⢦⣭⣿⣷⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⢳⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⣿⡇ ⡀⠙⠲⣝⠿⣦⣀⠙⠺⣕⡦⡈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢀⣾⣿⡇ ⡓⢤⡀⠀⠙⠪⣝⠳⣦⣀⠉⢲⣼⣿⣿⣿⣾⣭⣽⣿⡿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠑⢶⣿⣿⣿⣿⡛⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇ ⣟⢦⣍⠲⢤⡀⠀⠙⢢⣭⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣦⣤⣄⠉⠢⡄⠀⠀⠀⢸⣿⣿⣿⢹⣿⣄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣇ ⠈⠓⢮⣝⣦⣿⣶⣿⣟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡌⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠙⠻⣿⣤⡈⠳⣄⠀⢸⣿⣿⣿⢸⣿⣿⣷⣦⡀⣠⡾⣿⣿⣿⣿⣿⣸ ⣭⣶⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⠻⡟⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⠀⠈⠻⣿⣄⠈⢦⣸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣦⠀⠈⢦⠀⠀⠘⣿⣷⠀⢹⣿⣿⣿⢸⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⡿⠿⠿⣏⠉⠑⣴⣿⣿⣿⣿⣿⣯⣿⣿⣿⠈⠉⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⣧⠀⠈⡇⠀⠀⠈⢿⠧⠸⣿⣿⣿⣾⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⡟⣾ ⣿⡿⠯⣉⠻⣦⣄⠀⠀⣡⣾⣿⣿⣿⣿⢟⣷⣿⣿⣿⣿⢶⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠨⠉⠀⠀⡇⠀⠀⠀⠈⢳⡀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣹⡿ ⠳⣝⡲⣌⡓⠦⣈⣵⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⠀⠆⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣧⢿⣿⣿⡇⣿⢸⣿⣿⣿⣿⣽⣿⡇ ⢆⡀⠙⢺⣹⣾⣿⣿⣿⣿⣿⣿⣷⠿⠿⠿⠿⣿⣿⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣀⣽⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⠶⠒⠒⣶⡿⣿⣇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠻⠛⠉⠀⠀⠀⠀⠈⣿⣿⣿⡏⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠎⠀⠀⡠⠊⣡⠎⠁⠉⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⠀⢸⠀⠀⡼⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⣿⡿⠿⠻⢏⣀⣾⣿⣿⣿⡀⢸⡄⢰⡇⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢛⣛⣒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠛⠲⠀⠀⢠⣿⣿⣿⣿⡿⣧⡀⠹⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡞⠋⠀⠀⠈⠙⠲⠤⢄⣀⡤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣽⣿⣿⣿⣟⣿⣿⠀⠀ ⢄⠀⢀⣴⣿⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠟⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣤⡤⢤⣉⠳⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⡟⠀⢰ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⢸⠀⢸⣀⠀⠀⠀⠀⠀⠀⡞⠀⡼⠋⠸⠀⠀⠈⣣⣈⣇⣀⣤⣴⣿⣿⣿⣿⣷⣿⣿⣿⢟⣿⣿⣿⣿⡇⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡟⠀⠈⢛⠦⣼⡄⠸⡄⠀⠀⠀⠀⠀⢰⠃⣸⠁⢰⡞⠛⠛⠛⠄⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣟⣵⣿⣿⣿⣿⣿⠇⠀⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⠃⠀⣠⠏⠀⢸⣟⠦⠽⠦⣄⡀⠀⠀⢸⠀⣿⠀⠸⡏⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣯⣾⣿⣿⣿⢹⣿⣿⣿⠀⠀⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢦⡀⠀⢸⠀⡰⠃⠀⢀⢸⠘⢦⣀⡀⠀⠙⠳⢤⣈⠇⠙⣧⠀⢉⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⢋⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⠀⠀⡯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠀⢄⣈⣳⣾⣼⣁⡚⠉⠀⢸⠀⢀⣈⣹⣄⣀⣁⣤⣭⣧⣤⣴⣾⣿⣿⣿⣿⣿⡿⠿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡇⠀⢠⢞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡤⠔⠊⠉⠁⣠⡿⠏⠻⣍⣉⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⣠⠞⠁⠀⠀⢰⣿⣿⣿⣿⣻⣿⣿⢻⣿⣿⣿⡇⠀⠸⣫ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⣿⡁⠀⠀⣠⠴⡚⠁⣇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⠃⠀⣘⡴ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⡼⠁⡇⠙⡶⠋⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⡟⠉⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣳⣿⣿⣿⣽⣿⣿⣿⣻⠀⠀⠏⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⡼⠁⠀⡇⢠⠃⣀⣴⣿⣿⣿⣿⣿⡿⠿⠛⠛⠙⠸⡀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣳⣿⣿⣿⢧⣿⣿⣿⢯⡇⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢀⡴⣩⣤⡶⣿⡿⢿⣿⣧⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣧⣴⣿⠀⠀⠀⠀⢠⠟⣦⣿⣆⣙⣏⣴⣦⣽⠿⢧⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠳⢾⠀⠀⠀⠀⢸⣼⡋⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣠⣄⠀⠀⠀⠀⢸⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢁⠘⠉⡇⠀⠀⠀⢀⣿⡏⠀⣀⣤⣤⣰⠄⢀⣤⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠒⢻⠀⠀⡗⠢⣄⠀⢸⣿⣧⠈⠛⠛⠿⠋⢄⣿⠉⠉⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠶⣾⠀⠰⣿⠒⢾⣿⣮⣿⣽⣦⠀⠀⢀⣠⡄⢸⣷⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⢹⡄⠿⠆⠀⠀⠀⢠⠷⣌⡇⠙⣯⠑⣤⣿⣀⡩⠿⢿⣿⠂⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⢸⠟⠂⠸⡀⠀⠀⢈⠀⠸⣇⣴⣿⢦⡈⠀⠙⣷⣞⣿⡟⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠉⠀⠀⠀⠃⠀⠀⠉⠀⠀⣿⣿⣿⣄⠙⢤⡀⠈⠛⠉⢀⣼⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠈⠓⠒⣲⠿⣼⣿⣷⣼⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣠⡴⠿⣾⣽⣽⡇⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⣠⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⣈⠴⢋⣿⣿⣿⣿⣿⣿⣏⠋⠀⠀⠈⠙⣾⢧⡀⠀⢹⣿⣿⣿⣦⣶⣶⢿⣛⣛⣉⠉⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠾⠓⠒⢉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣼⡷⡿⡿⠛⠛⣻⣿⣿⣿⠿⠿⠹⣿⡛⢻⣷⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⢸⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠛⠋⢉⣽⣷⣶⡄⢿⣆⠀⣿⡇⢿⣇⣀⡀⠀⢻⣷⢿⣿⡄⢻⡇ ⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⡿⠿⣿⠛⠋⢩⣯⢹⣿⡿⠟⠋⠀⠀⠸⣿⠀⢹⣿⠈⢿⣆⣿⡇⠸⣿⠋⠁⠀⠸⣿⡀⢹⣷⠸⣷ ⣶⡶⠿⢛⣛⣉⠉⢁⣼⣷⣶⡄⢿⣷⣤⣾⣿⡄⣿⣦⣤⡄⠀⠀⠀⣿⡆⠀⣿⡆⠈⢿⣿⡇⠀⢿⠷⠿⠟⢀⣙⣡⣤⣤⡶⠿ ⢸⣧⢠⣿⠛⢻⣷⢸⣿⠀⢹⣷⢸⣿⠻⠟⢹⣇⢸⣿⠁⣀⣀⠀⠀⠘⠿⠶⠟⠁⣀⣈⣉⣤⣤⡶⠶⠾⠛⠛⠋⠉⠁⠀⠀⠀ ⠈⣿⠈⣿⡄⣤⣶⡄⣿⡿⠛⣿⡆⣿⡆⠀⠘⣿⠌⠿⠟⢛⣋⣠⣤⣴⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠹⣧⣨⣿⠇⠸⡧⠀⠙⣇⣘⣡⣤⣤⣶⠶⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣀⣈⣩⣥⣴⡶⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀ ⢰⡿⠋⠙⠦⣄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⢳⣄⠀ ⠸⣧⠀⠀⠀⠈⣷⣤⣤⠛⠋⠛⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣷⡄⠀⠀⠛⡆ ⠀⠙⣷⠀⠀⠀⠀⠀⡇⠀⠀⣴⠛⠀⠀⠀⠀⠀⣠⣴⡿⠓⠛⠛⢿⣟⠒⢤⣄⠀⠀⠀⠀⢾⡏⠀⠈⢿⣿⠃⠀⠠⠀⢸ ⠀⠀⢸⡄⠀⠀⠚⠋⠁⠀⣼⠁⠀⠀⠀⢀⡴⠛⠛⣋⣤⣄⠀⠠⠤⢤⣀⠀⠈⠳⢦⡀⠀⠈⢳⡀⠀⣾⠃⠀⣀⡀⠀⢺ ⠀⠀⠀⢿⡀⠀⠀⠀⡀⠀⣿⠀⠀⠀⣴⠋⠡⠂⠉⠀⠀⠀⣀⣀⡀⠀⠉⠙⠀⠀⠈⠱⣆⠀⢸⡇⢀⠀⠀⠠⠋⠁⢀⡿ ⠀⠀⠀⠈⢧⡀⠀⠀⠈⣰⠏⠀⠀⡾⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠙⡆⠸⣦⡀⠀⠀⠀⢀⣠⠟⠁ ⠀⠀⠀⠀⠀⠙⢦⣤⣴⠟⠀⠀⣸⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⡄⠈⠻⣦⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣷⡀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⡤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠿⣦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠂⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⢸⣆⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠈⢣⡉⠉⠙⠚⠙⢷⠀⠀⠀⠀⣰⢾⠓⠛⠉⢉⡽⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⣹⣧⣆⣠⣀⡼⣆⠀⢀⣴⢿⣲⣤⣤⡤⡏⠀⠀⠘⣆⠀⠀⠀ ⠠⣀⡴⠃⠀⠀⣴⡿⠙⢿⣇⡀⠀⠸⣎⢨⠏⠀⠀⣁⡼⠁⢱⡀⠀⠀⠘⢦⣀⡤ ⠀⠈⢿⠲⢤⣰⠟⢁⣠⣾⠿⣿⣿⣯⣿⣯⠿⣿⣿⡿⣟⠀⠀⠑⣤⠤⠒⡿⠁⠀ ⠀⠀⠈⢧⠀⠹⡉⢻⣟⣻⣆⣩⣾⣍⣿⡿⣄⣾⣟⢀⣿⣶⠞⢉⠇⠀⡼⠁⠀⠀ ⠀⠀⠀⢸⡂⢀⣇⠀⣹⠉⠛⣿⣿⡿⢿⡿⣿⣿⣿⠋⣠⡿⡆⢸⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⢸⡁⣼⣿⣿⣟⣷⣾⠿⣿⣦⠀⣠⣴⣿⣿⠿⣿⣻⣁⣘⣄⠠⡇⠀⠀⠀ ⠀⠀⠈⠉⠛⢬⡉⠒⠿⣋⠙⣷⣬⠿⣷⣾⢿⣇⣽⣿⣣⠔⠒⠉⡬⠟⠉⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⢆⣼⠟⣶⡸⣟⡾⢽⣿⡟⠁⠀⣰⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡼⠿⢧⡟⢷⣯⢱⡬⠿⢿⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠙⣿⣻⠇⠀⠀⢈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠓⢦⣀⠘⡏⢀⡴⠚⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣬⣿⣿⡿⠿⠛⠻⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠞⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠙⠰⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡄⠀⣀⣤⠴⠶⠖⠒⠒⠒⢶⣦⣀⠀⠀⠀⠸⣎⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣷⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢹⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢺⣿⣿⣿⠃⡀⠰⠃⢸⣶⣦⣴⡤⠀⠀⠀⠀⡆⠘⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠙⠋⠉⠁⠁⠀⠐⠛⠿⠛⠋⡁⢀⣠⡶⠄⠁⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠄⠐⠀⠈⢧⣠⡴⠀⣀⠀⠈⣳⡿⠿⢭⣁⡆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⣀⣿⣷⣼⣿⣮⣶⣶⣶⡾⣯⣗⢦⣾⠟⠁⠀⠀⣺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣯⡽⢿⣿⣄⣿⣉⣻⣏⣻⣼⠿⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣄⠀⠀⠉⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⢀⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢿⠁⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢿⡄⣽⣷⣤⣀⠀⠀ ⠀⠀⣴⠟⣿⣿⡇⠰⣶⣀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢀⣼⠿⣯⡀⡄⠙⣷⣄ ⢀⣼⣿⣼⠋⢸⣿⣀⣿⣿⠆⠀⠀⢀⣤⡿⠋⠀⢀⣰⣿⣿⣾⡿⣦⣙⣾⣷⣿ ⠘⠏⠛⠁⠀⢸⣿⣿⣿⣿⣦⣤⡖⠛⠁⠀⠀⣰⣿⣿⣿⡟⠉⠀⠈⢿⣿⠿⠃ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠛⠋⠉⢉⣭⡽⢾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣻⣿⣦⣤⣼⡟⠉⠂⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢦⡒⣿⣿⠛⠿⠿⠻⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣎⣻⣿⣿⠆⠀⠀⠀⢻⡆⠠⠈⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠿⠦⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣀⣤⣤⣶⣶⣿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠉⢉⣉⣉⣉⠉⠛⢶⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⡾⠟⢋⣉⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣽⣿⣿⣿⣷⡌⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣽⣦⣾⣿⣿⣿⡿⢿⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡿⠻⣿⣿⣿⣿⣿⢿⣧⠰⡇⠀⠀⣀⠀ ⠀⠀⠀⢻⣷⣿⣿⣿⣿⣥⣿⠇⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣻⣿⣿⣿⡟⣸⠀⢣⢀⣽⣿⠇ ⢠⣶⠀⢸⣿⣝⠿⢿⣿⣿⣧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠁⠀⠀⠁⠀⣾⠀ ⠸⡆⠉⠛⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡠⢷⡀⠀ ⠀⠀⢀⡿⣙⡄⠀⠀⠀⢠⣤⣤⡀⢀⡤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣶⠞⠋⠁⠀⠀⠀⠀⣾⠉⠀⣸⡇⠀ ⠀⠀⢸⡇⠈⠉⢇⠀⠀⠀⠀⠈⠙⠛⡷⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⢀⣽⠇⠀ ⠀⠀⠘⣇⠢⠀⢾⢦⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠉⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⢰⣶⡆⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢀⣾⣿⠟⢿⣿⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠛⠁⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⢻⣿⣧⠀⠀ ⠀⣾⣿⡏⠀⠈⣿⣿⣧⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠃⠀⢹⣿⣧⠀ ⢰⣿⣿⣷⡄⠀⢹⣿⣿⠀⠀⠘⣿⣧⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⡟⠀⠀⣼⣿⣿⡆ ⣼⣿⠛⢿⣧⠀⠈⢿⣿⣇⠀⠀⢻⣿⣦⠀⢰⣿⣿⡏⠀⣹⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⠃⠀⣸⣿⢻⣿⣇ ⣿⣿⠀⢸⣿⣆⠀⠈⣿⣿⣧⡀⠀⠙⣿⣷⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⠃⠀⢠⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⡄⠀⠈⢻⣿⣿⣦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣴⣿⣿⡿⠁⠀⢀⣾⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣦⡀⠀⠉⠻⢿⣿⣿⣶⣦⣄⠈⠉⠉⠉⠉⣠⣤⣶⣿⣿⡿⠟⠋⠀⢀⣴⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⣶⣦⣄⣀⡈⠉⠛⢿⣿⣷⡆⠀⢠⣾⣿⡿⠛⠉⠁⣀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣷⣦⣄⡙⢿⣿⠀⣸⣿⠋⣠⣴⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⠸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠙⢿⣿⣿⡟⠀⢸⣧⣾⡿⠋⠉⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⢰⣿⡿ ⢻⣿⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⡿⠁⠀⠈⢻⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⡇ ⢸⣿⡇⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠙⢿⣿⠋⠉⠉⠛⠛⠛⠛⠛⠛⠁⠀⠀⢸⣿⡇ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣤⡀⠀⠀⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣧⣄⣀⣤⣿⣦⣀⣠⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀ ⠀⠀⢻⣿⣇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣼⣿⡟⠀⠀ ⠀⠀⠈⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠀⠀⠀⣰⣿⡿⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⡄⠀⠀⣿⣿⣿⠏⠁⠀⠈⠛⠻⠟⠋⠉⠙⠻⠟⠛⠁⠀⠀⠹⣿⣿⣿⠀⠀⢠⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣆⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣰⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣶⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢡⣾⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣄⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⢀⣀⣀⣀⣀⠀⠀⠀⡄⡤⣤⡄⢠⢠⠤⠠⡄⢤⢠⡠⠤⠀⠀ ⠀⠀⠘⢛⠛⠓⠛⠃⠚⠒⠁⠘⠛⠚⠛⠓⠛⠒⠛⠚⠚⠃⠓⠉⠀⠀⠓⠘⡁⠚⠓⠛⠒⠓⠛⠒⠓⠓⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⣯⡷⠾⠛⠛⠛⠛⠛⠳⠶⢯⣗⡲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣵⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣍⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡙⣄⠀⠀ ⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⠏⠀⣠⣤⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⣆⠀ ⢠⢞⣥⣶⣌⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⡏⣠⡾⠟⠉⠁⠀⠀⠙⢻⣆⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠈⣿⡹⡄ ⡟⣾⣿⠁⣌⡻⢷⣦⣝⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣰⡟⠀⠀⠀⠀⠀⠀⣤⡀⣿⡆⢀⣤⡾⠟⠋⠉⠉⠻⢷⡄⠀⢸⡇⡇ ⠱⢝⡻⣷⣮⡛⠶⣌⡻⢿⣶⡿⣯⡱⡄⠀⠀⠀⠀⢸⣿⡏⣿⡇⠀⠀⠀⠀⠀⢠⣿⡷⣼⣷⡾⠋⠀⠀⣰⣦⠀⠀⠈⢿⡆⢸⡇⡇ ⠀⠀⠉⠲⢝⡻⣦⣌⡙⣾⡏⠀⢸⣧⣽⣽⣝⣦⡀⠈⡟⣷⢿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⠃⠀⠀⠀⣿⣿⡇⠀⠀⢸⡇⢸⣇⡇ ⠀⠀⠀⠀⠀⠈⠒⣝⣷⣿⠀⢠⣿⡟⠁⢨⡿⢿⣝⢦⣿⣻⡎⣿⣦⡀⠀⠀⠀⢀⣴⡿⢹⣿⠀⠀⠀⠀⠹⠿⠁⠀⠀⣾⠃⣾⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠘⣞⢿⡆⠀⠉⠀⠀⣾⠃⢠⡿⠷⣮⣛⢿⣍⢿⣿⣿⣿⣿⡟⢋⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⢏⣼⢳⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⠷⣄⡀⠀⠀⠁⢠⣿⡃⠀⠊⠈⡓⠿⣦⡀⠉⠉⢁⡾⠛⣻⢦⣻⣿⣦⣄⣀⣀⣤⣴⢟⣱⡿⣡⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢝⣳⢦⣤⣈⣿⣷⣏⣐⠀⣙⠃⣬⣿⠶⣄⣿⠀⢀⡁⠶⣄⡚⢽⣿⡿⠟⣫⣴⠟⣫⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠯⠽⠟⠮⣙⡿⢧⣮⡧⠁⡘⢮⣝⡷⠀⠙⠷⣮⣟⠷⢉⣿⠻⣯⣰⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢝⠷⣦⣙⠐⠈⡙⢷⣴⡟⣷⠉⣥⡾⢡⠀⢨⡿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⡽⣻⡦⣴⣼⢏⡸⠃⣴⣿⡿⢋⣴⢟⡽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⡵⣻⡿⢿⣮⢫⣿⣶⣼⢏⡀⣠⡟⠻⢮⣑⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣪⣷⣟⣵⠟⣫⡶⢊⣿⣿⣻⣷⣶⣽⣿⡋⠀⠈⠲⠍⡛⢶⣝⡢⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣫⣶⡿⠙⢿⣭⡷⣛⣥⡶⢛⣽⠿⢯⣼⣋⢿⡟⣿⡳⣦⣄⠂⠈⣸⡟⠙⢶⡍⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣯⢻⣷⣗⢄⣿⡿⣟⣽⡲⣿⣀⣀⠀⠈⠛⢷⣽⣦⣙⠶⣭⡻⢿⣏⡰⣢⣿⢇⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⢿⣿⡿⣟⡽⠚⠁⡾⣷⠿⠿⠿⣿⠷⠀⠀⠈⠉⠉⢷⢹⠈⠓⢭⣛⣛⡵⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠁⠀⠀⡼⣹⣿⣄⣀⣀⣠⡀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿⣫⣿⡿⠟⠁⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄⣿⣁⣀⣤⣶⠶⠶⠶⠶⠾⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠽⣯⠵⣚⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣴⣾⣿⣿⣿⣷⣶⣤⡈⠙⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⢰⣶⡆⠀⠀⠀⠀⢀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⡆ ⢀⠀⢸⣿⣧⣰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⣿⣿⣿⣇ ⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠛⠛⠛⢉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋ ⣶⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣥⣾⡿ ⠙⢿⣿⣷⣶⣬⣙⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣉⣥⣴⣾⣿⣿⣿⣿⡇ ⠀⠀⠙⣿⡟⢿⣿⣿⣿⣷⣶⣦⣬⣭⣉⣙⣛⣛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢛⣛⣛⣋⣩⣭⣭⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠟⠛⠛⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠀⢀⣤⡾⢷⣤⡀⠀⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠐⠾⠛⠉⢀⣀⠉⠻⠷⠂⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⢀⣠⣶⠟⠻⣶⣄⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠈⠉⢀⣴⣦⡀⠉⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⠀⢰⣦⠀⠀⠛⠁⠈⠛⠀⠀⣴⡆⠀⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⢙⣿⣶⡄⠀⠀⢠⣶⣿⡋⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⠆⠁⠀⠀⠀⠰⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⠿⠂⠐⠿⣶⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⠁⠐⠛⠛⠂⠈⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣼⣧⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣶⢶⣄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢟⣿⡿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⣾⣿⣿⠿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣝⢿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⢿⣟⢿⣿⣽⣿⡆⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⢷⣿⡾⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡞⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢻⣿⣷⡀⠀⠙⢿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠈⠋⠉⠸⠉⠹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠟⠉⢸⣿⣿⣿⡟⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⣿⣿⣿⠃⠀ ⠀⠀⢸⣿⣿⢿⣿⣿⠏⠻⣦⡠⣶⡿⢟⣩⣽⣷⣶⣶⣶⠤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣒⣛⡛⠛⡿⣄⠀⣿⣿⣿⠀⠀ ⠀⠀⠘⡏⡏⢀⣿⣿⠀⠀⠙⠿⢻⢃⣠⣴⠾⣿⣿⣿⣿⣿⣦⡉⠛⢻⡥⢤⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠆⣿⣿⠏⠀⠀ ⠀⠀⠀⢱⢧⠸⣿⣿⠀⠀⠀⠀⢸⠙⠛⢯⣀⣙⣛⣋⣬⣿⠟⢩⣿⡿⠀⠀⢰⣿⡿⠿⣏⣙⣿⣟⣣⣼⣿⠋⠀⠀⣽⡇⠀⠀⠀ ⠀⠀⠀⠈⣿⣆⣿⣿⡀⠀⠀⠀⠸⡄⠀⠀⠈⠉⡩⠭⠟⡿⠀⠸⣵⠃⠀⠀⠈⣿⣿⣄⠀⠉⠛⠛⠛⢹⠇⠀⠀⡼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡿⣿⣇⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⣀⣤⡞⠁⠀⠀⠀⠀⢸⣏⠻⣅⠀⠀⠀⠀⠀⣀⡠⠊⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠁⠀⠀⠀⠀⠀⢘⣿⡄⠀⠉⠉⠉⠉⠉⠀⠀⠀⡤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣤⣀⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡟⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢻⡿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣤⣦⣄⣀⠀⠀⠀⠀⢀⡏⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠫⣉⣉⡀⠀⠉⠁⢀⣉⡩⠙⠒⠂⢀⡿⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠛⠛⠛⠻⠶⠄⠀⠀⡤⢾⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠛⣿⣿⠈⠙⢿⣿⡀⠀⠙⠓⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠚⠁⠀⣸⠇⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣾⣿⡟⠀⢻⣿⡀⠀⠀⠈⠛⠲⢤⣀⡀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⣀⣴⡿⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀ ⣠⣴⣾⣿⣿⣿⣿⡇⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣴⠊⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠛⣻⡟⠻⢹⣿⡇ ⣸⣿⡿⠛⠁⠀⠈⢹⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣿⠇⠀⠈⠻⣿ ⣿⡟⠁⠀⠀⠈⡀⠸⣿⡀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⠈⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣯⡁⠀⠀⠀⠀⣸⡿⠀⢰⠀⠀⠹ ⡟⠀⠀⠠⠶⠤⠥⠀⢻⣷⡀⠀⢸⠃⢠⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡏⢱⣤⣴⣿⣿⣿⣿⣿⣿⣥⣄⠈⢻⡄⠀⠀⢰⣿⠃⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠤⢤⣤⣿⣷⣄⣸⡄⠈⠿⢿⠃⣨⡟⠻⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⡿⣏⠀⠻⣷⡿⠀⣸⡇⠀⣰⣿⠃⠀⣰⡇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡴⠶⠾⠿⠿⠿⠿⠿⣿⣶⣤⣾⣿⣥⣾⡿⠋⠉⠀⠀⠀⠈⠙⠟⢿⣷⣽⣷⣄⣀⣡⣾⢟⣠⣾⠟⠁⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠉⠛⠻⠿⠿⠿⠟⠛⠉⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠀⠀⠀⠐⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏⠀⠀⠀⠈⠿⠋⠉⠛⠛⠿⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠛⠛⠿⢿⣷⣶⣤⣤⣶⣶⣾⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⡿⠛⠛⠓⠒⠶⠦⢤⣿⡀⠀⠀⠀⢀⣠⣦⣀⣀⣀⣀⣴⣾⣿⡿⠟⠋⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⡴⠟⠋⠉⣉⣽⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀ ⣦⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠇⠀⠀ ⢻⣄⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⣠⣦⡀⢀⣀⣤⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠛⠁⠀⠀⠀ ⠘⣿⣦⡀⠀⠀⠉⠛⠻⠿⠷⠿⣿⣿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀ ⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀ ⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀ ⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆ ⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀ ⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀ ⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀ ⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢛⣿⡇⠹⣟⡂⠁⢠⣇⡝⢉⡀⠉⠁⠶⢤⣤⡈⠁⠑⠀⠃⢀⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⢀⣿⣇⣀⣠⣿⢿⣛⣿⣻⡷⠟⠃⠈⠙⠶⣶⡀⣸⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣼⣿⠿⠛⠉⠀⣀⣠⡤⢤⣄⣀⠀⠀⠀⠀⠈⢉⣩⠽⠯⢿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠒⠀⢀⡵⠛⠉⠀⠀⠀⠀⠈⠙⢶⣄⣴⠟⠉⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢐⣋⣩⠤⠆⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡶⠾⠿⠛⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⢸⡆⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⣷⢀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⢀⣀⠀⠒⠀⠀⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⢁⡾⠻⢧⣄⠸⣿⣿⣿⡿⠀⠀⣸⠏⠈⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡟⣃⣀⣠⣄⠠⠤⠤⠀⠀⠀⡀⠙⡿⣷⣄⣀⣀⣀⢈⣻⣿⠷⠋⠀⠀⠀⠉⠙⠾⣿⣉⣠⣤⣾⠏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠋⠉⢉⣈⣁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠨⣭⣍⠛⠿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣟⡛⠭⣭⠤⠀⠀⠀⠀⠀⠀⠙⠛⢷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⡤⠤⠔⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣧⠀⡀⠀⠀⠠⠔⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠲⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣯⣤⣤⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣜⣉⣁⣀⣠⣤⣤⣤⣀⣠⣤⣀⣤⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣫⣄⣀⣀⠀⠉⢿⣿⣧⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠛⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣩⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠉⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠹⠇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⡗⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣏⢹⣧⡄⢙⣤⡄⢤⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⢻⡏⢛⢧⣘⣿⡮⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⠋⠀⠟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⢷⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠏⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣨⣯⣤⣤⣴⣤⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⠀⠀⠀⣴⠋⣡⡽⠋⠀⠀⢠⣿⣿⣿⣿⣿⠿⠟⢋⣹⣦⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⡌⠻⣷⣀⣾⣇⣾⡿⠃⠀⠀⢠⠟⠀⢰⡿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣬⡾⠿⠟⣿⡆ ⠀⠈⠳⢼⣿⡟⠛⡏⠀⠀⢀⠴⠛⠒⣒⠻⣄⢀⣠⣤⠲⡖⠶⢞⡛⠃⠤⣈⠁⢲⡿⠀ ⠀⠀⠀⠀⢹⠀⣄⠉⠀⠰⠁⠀⣴⣿⣿⣿⣾⣯⠉⠁⠀⢹⠦⡀⠈⠲⣄⠀⣹⡟⠁⠀ ⠀⠀⠀⠀⠘⡄⠈⠦⡀⠸⡀⠈⢿⣿⣿⣿⡿⣽⡀⠀⠀⢸⣧⠙⡄⠀⢈⣷⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⢰⣶⡾⣦⣄⣉⣻⣽⠞⠙⢿⡄⠀⣸⢸⣀⣵⡶⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⡀⠻⡝⢿⣿⣿⣟⣛⡀⠀⠀⠛⣶⢛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠉⣦⣌⣦⠙⠯⠛⠻⡄⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⢻⣿⣿⣶⣿⣦⣸⣿⣿⠿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⣿⣿⣿⣿⣿⣟⣛⣽⣷⡾⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢃⠇⢸⢾⣭⣭⣭⣍⣛⣻⣿⣿⣷⠿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣷⠃⣰⣿⣷⣦⣤⣉⡉⠛⢛⣛⣩⣥⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⡇⠀⣿⡙⢶⣬⣙⣻⣻⣿⣟⣯⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣷⠀⣿⣟⢷⣿⡿⠛⠛⠛⠿⢿⣿⣿⣾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣧⣸⣿⣿⣞⠙⠛⠶⣶⣾⡿⠿⢋⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣀⣀⡀⠀⠈⠻⢻⣿⣿⣿⣶⡞⠙⣿⣧⢾⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠿⣿⣿⣿⣿⠉⢹⣿⣿⡇⠀⣿⡿⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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